Properties

Label 5445.2.a
Level $5445$
Weight $2$
Character orbit 5445.a
Rep. character $\chi_{5445}(1,\cdot)$
Character field $\Q$
Dimension $181$
Newform subspaces $56$
Sturm bound $1584$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5445.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 56 \)
Sturm bound: \(1584\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(2\), \(7\), \(23\), \(53\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5445))\).

Total New Old
Modular forms 840 181 659
Cusp forms 745 181 564
Eisenstein series 95 0 95

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(5\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(18\)
\(+\)\(+\)\(-\)\(-\)\(18\)
\(+\)\(-\)\(+\)\(-\)\(18\)
\(+\)\(-\)\(-\)\(+\)\(18\)
\(-\)\(+\)\(+\)\(-\)\(30\)
\(-\)\(+\)\(-\)\(+\)\(25\)
\(-\)\(-\)\(+\)\(+\)\(24\)
\(-\)\(-\)\(-\)\(-\)\(30\)
Plus space\(+\)\(85\)
Minus space\(-\)\(96\)

Trace form

\( 181q - q^{2} + 175q^{4} - q^{5} - 4q^{7} - 9q^{8} + O(q^{10}) \) \( 181q - q^{2} + 175q^{4} - q^{5} - 4q^{7} - 9q^{8} - 3q^{10} - 10q^{13} - 24q^{14} + 159q^{16} + 6q^{17} - 12q^{19} - 7q^{20} - 8q^{23} + 181q^{25} + 10q^{26} + 12q^{28} - 6q^{29} + 4q^{31} - 29q^{32} + 6q^{34} + 4q^{35} - 2q^{37} + 12q^{38} - 3q^{40} + 14q^{41} - 16q^{43} + 28q^{46} - 28q^{47} + 169q^{49} - q^{50} + 10q^{52} - 26q^{53} - 4q^{56} + 50q^{58} - 16q^{59} + 6q^{61} + 32q^{62} + 191q^{64} + 2q^{65} - 20q^{67} + 66q^{68} + 16q^{70} + 12q^{71} - 22q^{73} - 14q^{74} + 44q^{76} - 32q^{79} + q^{80} + 82q^{82} - 14q^{85} + 32q^{86} - 42q^{89} - 48q^{91} - 4q^{92} + 76q^{94} + 12q^{95} - 114q^{97} + 55q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5445))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 11
5445.2.a.a \(1\) \(43.479\) \(\Q\) None \(-2\) \(0\) \(-1\) \(-3\) \(+\) \(+\) \(-\) \(q-2q^{2}+2q^{4}-q^{5}-3q^{7}+2q^{10}+\cdots\)
5445.2.a.b \(1\) \(43.479\) \(\Q\) None \(-2\) \(0\) \(1\) \(3\) \(+\) \(-\) \(-\) \(q-2q^{2}+2q^{4}+q^{5}+3q^{7}-2q^{10}+\cdots\)
5445.2.a.c \(1\) \(43.479\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}+2q^{13}+\cdots\)
5445.2.a.d \(1\) \(43.479\) \(\Q\) None \(-1\) \(0\) \(-1\) \(3\) \(-\) \(+\) \(-\) \(q-q^{2}-q^{4}-q^{5}+3q^{7}+3q^{8}+q^{10}+\cdots\)
5445.2.a.e \(1\) \(43.479\) \(\Q\) None \(-1\) \(0\) \(1\) \(2\) \(-\) \(-\) \(+\) \(q-q^{2}-q^{4}+q^{5}+2q^{7}+3q^{8}-q^{10}+\cdots\)
5445.2.a.f \(1\) \(43.479\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(q-2q^{4}+q^{5}-q^{7}+2q^{13}+4q^{16}+\cdots\)
5445.2.a.g \(1\) \(43.479\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(q-2q^{4}+q^{5}+q^{7}-2q^{13}+4q^{16}+\cdots\)
5445.2.a.h \(1\) \(43.479\) \(\Q\) None \(1\) \(0\) \(-1\) \(-3\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{4}-q^{5}-3q^{7}-3q^{8}-q^{10}+\cdots\)
5445.2.a.i \(1\) \(43.479\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}-2q^{13}+\cdots\)
5445.2.a.j \(1\) \(43.479\) \(\Q\) None \(1\) \(0\) \(1\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
5445.2.a.k \(1\) \(43.479\) \(\Q\) None \(2\) \(0\) \(-1\) \(3\) \(+\) \(+\) \(-\) \(q+2q^{2}+2q^{4}-q^{5}+3q^{7}-2q^{10}+\cdots\)
5445.2.a.l \(1\) \(43.479\) \(\Q\) None \(2\) \(0\) \(1\) \(-3\) \(+\) \(-\) \(-\) \(q+2q^{2}+2q^{4}+q^{5}-3q^{7}+2q^{10}+\cdots\)
5445.2.a.m \(2\) \(43.479\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(4\) \(-\) \(-\) \(-\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(2+\cdots)q^{7}+\cdots\)
5445.2.a.n \(2\) \(43.479\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(-2\) \(-4\) \(+\) \(+\) \(-\) \(q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}-2q^{7}+\cdots\)
5445.2.a.o \(2\) \(43.479\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(2\) \(2\) \(-\) \(-\) \(-\) \(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(2-2\beta )q^{7}+\cdots\)
5445.2.a.p \(2\) \(43.479\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(2\) \(4\) \(+\) \(-\) \(-\) \(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+2q^{7}+\cdots\)
5445.2.a.q \(2\) \(43.479\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q-2q^{4}+q^{5}-\beta q^{7}+4q^{16}-2\beta q^{17}+\cdots\)
5445.2.a.r \(2\) \(43.479\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q+\beta q^{2}+q^{4}-q^{5}-2\beta q^{7}-\beta q^{8}+\cdots\)
5445.2.a.s \(2\) \(43.479\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(-4\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+q^{4}+q^{5}-2q^{7}-\beta q^{8}+\beta q^{10}+\cdots\)
5445.2.a.t \(2\) \(43.479\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+\beta q^{2}+q^{4}+q^{5}-\beta q^{8}+\beta q^{10}+\cdots\)
5445.2.a.u \(2\) \(43.479\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+\beta q^{2}+q^{4}+q^{5}+\beta q^{7}-\beta q^{8}+\beta q^{10}+\cdots\)
5445.2.a.v \(2\) \(43.479\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(-2\) \(4\) \(+\) \(+\) \(-\) \(q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}+2q^{7}+\cdots\)
5445.2.a.w \(2\) \(43.479\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(2\) \(-4\) \(+\) \(-\) \(-\) \(q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}-2q^{7}+\cdots\)
5445.2.a.x \(2\) \(43.479\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(2\) \(-2\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-2+2\beta )q^{7}+\cdots\)
5445.2.a.y \(2\) \(43.479\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(4\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}+2q^{7}+\cdots\)
5445.2.a.z \(3\) \(43.479\) 3.3.148.1 None \(-1\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.ba \(3\) \(43.479\) 3.3.469.1 None \(-1\) \(0\) \(-3\) \(3\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.bb \(3\) \(43.479\) 3.3.404.1 None \(-1\) \(0\) \(3\) \(-1\) \(-\) \(-\) \(-\) \(q-\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.bc \(3\) \(43.479\) 3.3.469.1 None \(1\) \(0\) \(-3\) \(-3\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.bd \(3\) \(43.479\) 3.3.404.1 None \(1\) \(0\) \(3\) \(1\) \(-\) \(-\) \(-\) \(q+\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.be \(4\) \(43.479\) 4.4.725.1 None \(-5\) \(0\) \(4\) \(-2\) \(-\) \(-\) \(+\) \(q+(-2+\beta _{1}+\beta _{2})q^{2}+(3-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
5445.2.a.bf \(4\) \(43.479\) 4.4.725.1 None \(-3\) \(0\) \(-4\) \(6\) \(-\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
5445.2.a.bg \(4\) \(43.479\) 4.4.2525.1 None \(-3\) \(0\) \(-4\) \(11\) \(-\) \(+\) \(+\) \(q+(-1-\beta _{3})q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\cdots\)
5445.2.a.bh \(4\) \(43.479\) 4.4.48704.2 None \(-2\) \(0\) \(4\) \(-4\) \(+\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}+q^{5}+\cdots\)
5445.2.a.bi \(4\) \(43.479\) 4.4.725.1 None \(-1\) \(0\) \(4\) \(3\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
5445.2.a.bj \(4\) \(43.479\) \(\Q(\zeta_{15})^+\) None \(-1\) \(0\) \(-4\) \(0\) \(-\) \(+\) \(+\) \(q+(\beta _{2}+\beta _{3})q^{2}+\beta _{1}q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
5445.2.a.bk \(4\) \(43.479\) 4.4.5725.1 None \(-1\) \(0\) \(4\) \(-8\) \(-\) \(-\) \(+\) \(q+(\beta _{1}-\beta _{2})q^{2}+(3-\beta _{2}-\beta _{3})q^{4}+q^{5}+\cdots\)
5445.2.a.bl \(4\) \(43.479\) \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(0\) \(4\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{3}q^{2}-\beta _{2}q^{4}+q^{5}+2\beta _{1}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)
5445.2.a.bm \(4\) \(43.479\) 4.4.27648.1 None \(0\) \(0\) \(-4\) \(0\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{3}q^{7}+\cdots\)
5445.2.a.bn \(4\) \(43.479\) 4.4.27648.1 None \(0\) \(0\) \(4\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}-\beta _{3}q^{7}+\cdots\)
5445.2.a.bo \(4\) \(43.479\) 4.4.8112.1 None \(0\) \(0\) \(-4\) \(0\) \(-\) \(+\) \(+\) \(q-\beta _{2}q^{2}+(2-\beta _{3})q^{4}-q^{5}-\beta _{1}q^{7}+\cdots\)
5445.2.a.bp \(4\) \(43.479\) 4.4.725.1 None \(1\) \(0\) \(4\) \(-3\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
5445.2.a.bq \(4\) \(43.479\) \(\Q(\zeta_{15})^+\) None \(1\) \(0\) \(-4\) \(0\) \(-\) \(+\) \(-\) \(q+(-\beta _{2}-\beta _{3})q^{2}+\beta _{1}q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)
5445.2.a.br \(4\) \(43.479\) 4.4.5725.1 None \(1\) \(0\) \(4\) \(8\) \(-\) \(-\) \(-\) \(q+(-\beta _{1}+\beta _{2})q^{2}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
5445.2.a.bs \(4\) \(43.479\) 4.4.48704.2 None \(2\) \(0\) \(-4\) \(-4\) \(+\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
5445.2.a.bt \(4\) \(43.479\) 4.4.725.1 None \(3\) \(0\) \(-4\) \(-6\) \(-\) \(+\) \(+\) \(q+(1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
5445.2.a.bu \(4\) \(43.479\) 4.4.2525.1 None \(3\) \(0\) \(-4\) \(-11\) \(-\) \(+\) \(-\) \(q+(1+\beta _{2}-\beta _{3})q^{2}+(2-\beta _{1}-\beta _{3})q^{4}+\cdots\)
5445.2.a.bv \(4\) \(43.479\) 4.4.725.1 None \(5\) \(0\) \(4\) \(2\) \(-\) \(-\) \(-\) \(q+(2-\beta _{1}-\beta _{2})q^{2}+(3-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
5445.2.a.bw \(6\) \(43.479\) 6.6.74043072.1 None \(0\) \(0\) \(-6\) \(0\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}-\beta _{4}q^{7}+\cdots\)
5445.2.a.bx \(6\) \(43.479\) 6.6.27433728.1 None \(0\) \(0\) \(-6\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{7}+\cdots\)
5445.2.a.by \(6\) \(43.479\) 6.6.74043072.1 None \(0\) \(0\) \(6\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+\beta _{4}q^{7}+\cdots\)
5445.2.a.bz \(6\) \(43.479\) 6.6.437199552.1 None \(0\) \(0\) \(-6\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.ca \(8\) \(43.479\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(0\) \(-8\) \(8\) \(+\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
5445.2.a.cb \(8\) \(43.479\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(0\) \(8\) \(-8\) \(+\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
5445.2.a.cc \(8\) \(43.479\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(0\) \(-8\) \(-8\) \(+\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+\cdots\)
5445.2.a.cd \(8\) \(43.479\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(0\) \(8\) \(8\) \(+\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5445))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5445)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1089))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1815))\)\(^{\oplus 2}\)